Presented here is part of the graduate work that I am doing in the much broader area of protocol analysis (see A.I. memo 137). The goal of the function abstraction is to find a procedure that satisfies a given set of fragmentary protocols. Thus functional abstraction is the inverse operation to taking a set of protocols of a routine. The basis technique in functional abstraction (which we shall call IMAGE) is to find a minimal homomorphic image of a set of fragmentary protocols. It is interesting to note that the technique of finding a minimal homomorphic image is the same one used to compute the schematized goal tree in A.I. memo 137. We define (a less than b) to mean that a is erased and b is written in its place. We shall use (a:b) to mean that the value of b is a.
